Problem: Simplify the following expression: $x = \dfrac{4q^2 + 36q + 32}{q + 1} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $4$ , so we can rewrite the expression: $ x =\dfrac{4(q^2 + 9q + 8)}{q + 1} $ Then we factor the remaining polynomial: $q^2 + {9}q + {8} $ ${1} + {8} = {9}$ ${1} \times {8} = {8}$ $ (q + {1}) (q + {8}) $ This gives us a factored expression: $\dfrac{4(q + {1}) (q + {8})}{q + 1}$ We can divide the numerator and denominator by $(q - 1)$ on condition that $q \neq -1$ Therefore $x = 4(q + 8); q \neq -1$